84 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

160. Th. a || & 1. Every integer is prime to one and to
minus one.

161. Th. The only integers to which zero is prime are one
and minus one.

T s bbb cDallc

If two integers are prime to each other, each 1is prime to any
factor of the other.

Example. 3 114> 2. 3112

163. Th. Ifa>>band |b| —= 1, then a—]11 b.
Example. 6> 3. 6-1] 3.

164. Th. If a—>> b and b is prime, then |b| —= 1 and
a ]l b.
Example. 8-> 3. 81| 3.

165. Th. Ifais prime,b—= 0,and
and a || b.
For example, 7 11 6, 5, 4, 3, 2, 1.

 

a| > |b|,then |a| > 1

GREATEST COMMON FACTOR

166. Def. a (X b stands for the greatest common factor,
or divisor, of @ and b, and is read ‘@ kor b.”
For example, 2(X 3 = 1, 608 = 2, (— 0Y(3 3 = 3.

167. Th. a—=0—b-=0Da®b=0Ra

168. Th. a>b>Da®b = ||
Example. 8 (— 4) = 4

169. Th. a1 =1
Example. 41 =1

170. Th. a-=0D2a X0 = |a|
Example. (—9) X0 =9

171. Th. (@1l d) = (aXRb=1)
Example. 4]19. 49 = 1.